Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 618, 735, 418 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 618, 735, 418 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 618, 735, 418 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 618, 735, 418 is 1.
HCF(618, 735, 418) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 618, 735, 418 is 1.
Step 1: Since 735 > 618, we apply the division lemma to 735 and 618, to get
735 = 618 x 1 + 117
Step 2: Since the reminder 618 ≠ 0, we apply division lemma to 117 and 618, to get
618 = 117 x 5 + 33
Step 3: We consider the new divisor 117 and the new remainder 33, and apply the division lemma to get
117 = 33 x 3 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 618 and 735 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(117,33) = HCF(618,117) = HCF(735,618) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 418 > 3, we apply the division lemma to 418 and 3, to get
418 = 3 x 139 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 418 is 1
Notice that 1 = HCF(3,1) = HCF(418,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 618, 735, 418?
Answer: HCF of 618, 735, 418 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 618, 735, 418 using Euclid's Algorithm?
Answer: For arbitrary numbers 618, 735, 418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.